Magnetohydrodynamic and bioconvective dynamics of Maxwell nanofluid with convective heating

Coupled heat, mass, and microorganism transport in electrically conducting non-Newtonian nanofluids is strongly affected by elastic stress relaxation, nanoparticle migration, and magnetic damping. A Maxwell fluid is therefore considered because its single relaxation-time parameter captures the elastic memory and stress-relaxation behavior that arise in rapidly stretched polymeric and bio-suspension flows, while retaining a tractable constitutive structure. This study investigates the steady magnetohydrodynamic bioconvective boundary-layer flow of a Maxwell nanofluid containing motile microorganisms over a linearly stretching sheet under convective heating. The model incorporates Maxwell viscoelasticity, Lorentz-force damping, Brownian diffusion, thermophoresis, viscous dissipation, heat generation/absorption, first-order chemical reaction, and microorganism-driven bioconvection. Similarity transformations reduce the governing partial differential equations to a coupled nonlinear boundary-value system, which is solved using the MATLAB bvp5c collocation solver. Grid-independence testing and comparison with published benchmark data confirm the numerical accuracy of the solution. The results identify the magnetic field as a dominant control mechanism: increasing the magnetic parameter suppresses the velocity field and simultaneously thickens the thermal, concentration, and microorganism boundary layers, thereby weakening the corresponding wall gradients. Increasing the Biot number raises the fluid temperature near the wall and enhances the local heat-transfer rate, whereas a higher Prandtl number produces a thinner thermal boundary layer and a larger local Nusselt number. In contrast, viscous dissipation, Brownian motion, and thermophoresis reduce the wall temperature gradient, while thermophoresis also weakens the local mass-transfer rate. The bioconvective Lewis number, Peclet number, and microorganism concentration-difference parameter substantially modify microorganism transport and near-wall accumulation. These findings provide a unified physical description of how magnetic control, viscoelastic relaxation, nanoparticle migration, and bioconvection jointly regulate surface transport in Maxwell nanofluid systems with convective heating.